It is proved that the free product state, in the reduced free product of C–algebras, is faithful if the states one started with are faithful. The reduced free product of C–algebras was introduced by Voiculescu as the appropriate construction for C–algebras in the setting of his theory of freeness [1]. (See also the book [2]). Given a set I and for each ι ∈ I a unital C–algebra Aι with a state φ...

Higher order generalizations of Lie algebras have equivalently been conceived as Lie n-algebras, as L∞-algebras, or, dually, as quasi-free differential graded commutative algebras. Here we discuss morphisms and higher morphisms of Lie n-algebras, the construction of inner derivation Lie (n+1)-algebras, and the existence of short exact sequences of Lie (2n + 1)-algebras for every transgressive L...

We study unitary multigraded non-associative algebras R generated by an ordered set X over a field K of characteristic 0 such that the mappings ∂k : xl → δkl, xk, xl ∈ X, can be extended to derivations of R. The class of these algebras is quite large and includes free associative and Jordan algebras, absolutely free (non-associative) algebras, relatively free algebras in varieties of algebras, ...

In this paper we study the structure of finitely presented Heyting algebras. Using algebraic techniques (as opposed to techniques from proof-theory) we show that every such Heyting algebra is in fact coHeyting, improving on a result of Ghilardi who showed that Heyting algebras free on a finite set of generators are co-Heyting. Along the way we give a new and simple proof of the finite model pro...

Several concepts of algebras with solutions of recursive equation systems are compared: CPO-enrichable algebras are proved to be iteration algebras of Z. Ésik, and iteration algebras are a special case of the recently introduced Elgot algebras (which are the monadic algebras for the free iterative monad). Another special case of iteration algebras are the iterative algebras of E. Nelson and J. ...